Re: st: A +ve log-likelihood!!

Amani <siyama@who.int> asks:
> I am running an "streg" model with a Lognormal distribution and the
> log-likelihood of the fitted model turns positive. I am not sure what
> happened here.
Two reasons this could happen (neither is an error):
1. In general -ml- with continuous responses, recall that the likelihood is a
probability DENSITY, not a probability. As such, when the scale is small
enough, the probability density can be greater than one, hence the likelihood
is greater than one, hence the log-likelihood is positive.
2. In -streg, lognormal()- a constant term (does not depend on the estimated
parameters) is added to the log-likelihood so as to make it directly
comparable to other log-likelihoods such as the Weibull and Exponential, which
themselves make the above constant-term adjustment so as to be invariant to
scale.
That is, we adjust Weibull and Exponential so that if you multiply the
survival times by a constant, you get the same log-likelihood. However, in
doing so, you have to make the same adjustment to log-normal and the other
-streg- models so that you can compare log-likelihoods across all, calculate
things like AIC and BIC, etc.
In any case, if Amani wants the actual based-on-probability-density
log-likelihood, he can do the following after running -streg, dist(lnormal)-
. gen temp = sum(_st*_d*ln(_t))
. scalar real_ll = e(ll) - temp[_N]
. di scalar(real_ll)
--Bobby
rgutierrez@stata.com
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/